Question on the third battle of Chattanooga!!!!!?

According to Peter Cozzens in "The Shipwreck of Their Hopes - The Battles for Chattanooga", historians classify three battles for Chattanooga, although in reality there was indeed one major one for the city itself, Chickamauga, which was even larger but outside the city, and a third distinct action after Chickamauga that entailed actions from as far away as Bridgeport, AL to the city itself. That action involved a strong reinforcement of Federal soldiers from Sherman, Hooker, and G.H. Thomas, who were entailed the job of dislodging the Confederates from Lookout Mountain, and more importantly opening the "Cracker Line", the supply line from the Federal depot in Bridgeport to the starving Union troops outside of Chattanooga. These actions were indirect actions that led to the major battle of Chattanooga, but are classified as the "third" battle that you may be looking for.

As far as I know there was one. And I was born and raised in Tennessee. The way your instructor is describing it, Chickamauga may have been the first. The siege of Chattanooga by Braggs Army the second. And the third would have been the "battle above the clouds", the real battle of Chattanooga. But the whole area was fought over well into 1864. A bunch of small unit actions that would be called battles today. Several hundred casualties on both sides is a major battle today. In the Civil War it was a skirmish.

to my knowledge there were only two, chattanooga and chickamunga